A few years ago, an experiment was made at Marlborough (1) to begin the teaching of statistics with a discussion of rank correlation because “within a few periods and without any complicated arithmetic, it was possible to discuss the main items in a statistician’s philosophy”. What I want to do in this article is to show how the same can be done with one of the commonest situations in elementary statistics, when we wish to compare populations from which two samples are drawn and decide whether one is “better” than the other. In the classical approach, this is often done by Student’s t test which is highly sophisticated compared with the Mann-Whitney U test, to which I now turn.

This article does not advocate dispensing with the calculus in the least; it suggests ways in which some of the traditional problems of calculus may be studied by other methods much earlier in the school. This makes a range of very interesting problems available to a much wider audience, and also shows how some of the problems of the sixth form science course can be treated with pupils who have the misfortune to be studying science without the calculus to help them.

Professor Geoffrey Matthews has described the scheme emanating from Ridgewaye School, Southborough, Kent, as a “Disaster Kit” and has asked me to write a description of it. This I gladly do because I am not sure about the title he has bestowed on it and you are invited to title it yourself when you have read my notes.

It is dangerous to generalize from unique experience, but the season of examination results is round again. Apart from the annual surprises, the ranked order is much as our departmental meetings predicted. The range of marks is similar and the percentage qualifying to proceed to Part II of the B.Ed, degree is of the same order. No one failed, but the tail is as abysmal as in previous years. These “tail” students are perhaps the most important ones, for they will teach over a wide band of education: the spectrum may start at the reception class in an infants school and end in the higher forms of a secondary or comprehensive school. Ability as a teacher doesn’t necessarily correlate with skill as a mathematician, but the quality of their contribution is questionable. So in this summer season efforts are again directed towards finding reasons for comparative failure.

The purpose of this article is to describe how we arranged a Gallup Poll for the North Norfolk Constituency some three weeks before the General Election. At the time of writing, the latter result is not known (and so this has been added later). The constituency itself is some 55,648 electors strong and, at the last General Election, Labour won the seat with a majority of approximately 700 in a straight fight with the Conservatives. It is therefore a highly marginal seat (although it has been Labour held for many years) and the result promised to be of some interest.

Numbers of the form n(n + 1)/2 are called triangular numbers. This is because and the left-hand side of this equation can be represented by a triangle as in Fig. (a). Numbers of the form n are called square numbers, or simply squares, for obvious similar reasons. We can also have rectangular numbers, but there is little point in defining them as numbers of the form m . n, since then they will include all the numbers. Instead we define a rectangular number as one which is of the form n(n + 1) —that is, the rectangle concerned must have one side exceeding the other by exactly one unit.

In studying an axiomatic subject, such as Group Theory, it is desirable to use the smallest set of axioms possible. In this short article we give three examples in which sets of classical axioms can be reduced.

In a raffle with replacement a number of prizes are available, and each winning ticket is replaced in the “hat” for inclusion in the draw for the next prize. Thus any ticket may win more than one prize.

The field of tape-recorders is ripe for some form of standardization. Except that speeds are supposed to be standardized (though a tape recorded on one model of a well-known make plays a semitone sharp on a newer model of the same make) most other things seem to be totally variable. This particular article was inspired by the frustration arising from the fact that some counters count the turns of the run-off spool, while others count the turns of the take-up spool. (Some counters only count every other turn; we shall ignore this wholly unnecessary complication.) The question is: how does one convert a reading from one type of counter to that from the other? This produces an unexpected graph in the form of a circular arc—a rarity which perhaps justifies a note.

The standard tape–recorder consists outwardly of two spools on which the magnetic tape is wound, from the left to the right, between least and greatest radii of a and b. On my machine, a is about 1.05 in. and b is about 2.75 in. Apart from what is on the tape, the only indication at any intermediate stage as to how much playing time is still left is provided by a revolution counter geared to the left hand spool, the one which starts full and finishes empty. The numbers registered are about half the actual number of revolutions made on the left: this arrangement allows some 1400 revolutions to be registered by only three digits. It can be assumed that the tape is fed out at a constant length per unit of time: so the time still to run is proportional to the length still to run. If the total number of revolutions to run is N, how much of the tape ha3 been run off when the reading is n?

It was encouraging to receive some letters following the article, in the 1969 December Gazette (Vol. LIII, No. 386), entitled “Playing with Probability”. Most of the letters made reference to the use of “a steam hammer to crack a walnut”. The purpose of the article was to review the teaching of probability at three levels in a secondary school, and since stochastic matrices are to be found in the further mathematics of the School Mathematics Project it seemed appropriate to give an example which used them. The fact that the particular example chosen could be answered in one line does not detract from the interest of the method used in the article—although, of course, as mathematicians we are always looking for elegance.